White House spokesman Trent Duffy said Bush called Bashir as he returned to Texas from a trip to New Mexico. Bush "stressed the need to keep the peace process moving forward at this delicate moment."
He welcomed President Bashir's commitment to implement the comprehensive peace agreement because it sends a positive message to the Sudanese people, Duffy said.
In addition, Bush underscored the importance of the Darfur peace talks in Abuha.
In the phone calls to Bashir and Rebecca Garang, widow of John Garang, Bush offered U.S. condolences over Vice President Garang's death in a helicopter crash on July 30.
Duffy said Bush thanked Mrs. Garang for calling for calm in Sudan. "The United States is resolved to continue supporting implementation of the comprehensive peace accord to honor her husband's vision," he said.
Garang died in a helicopter crash on July 30, three weeks after he was sworn in as vice-president. His death has raised fears a January deal to end 21 years of conflict in Sudan might collapse.
Bush thanked Rebecca Garang for the hope her husband brought to the Sudanese people for "a democratic united and peaceful nation," Duffy said.
The Ugandan presidential helicopter Garang was traveling in went down in bad weather in mountainous terrain and his supporters have said they do not suspect foul play. But Ugandan President Yoweri Museveni said the cause of the crash was unclear.
Asked if the United States suspected that the helicopter crash was not an accident, Duffy replied: "Not at this point."
The United States has sent officials from the National Transportation Safety Board to investigate the crash. He said the investigators were requested by the Sudanese and Ugandan governments.